Scattered data interpolation requires fitting of a smooth function or surface through a set of non-uniformly distributed data points. Inexplicit interpolation methods need to solve systems of equations. A widely used explicit interpolation method is Lagrange's polynomial interpolation, but oscillation at the edges of an interval that occurs when using Lagrange's polynomial interpolation with polynomials of high degree.
A new local explicit method for large scale scattered data approximation and interpolation that minimizes approximation error and processing time and transmits the information of scattered data to all positions in the domain smoothly will assist in advancing technological needs and solving technological problems.